Blackberry Puree:

Place the blackberries in the bowl of a food processor. Process until liquidy, about 1 minute. Transfer to a fine sieve suspended over a bowl. With a silicone spatula, stir the purée until all the juices have been strained and only the seeds are left behind. Discard seeds.

Transfer purée into a squeeze bottle and refrigerate until ready to use, up to 1 day.

Make the cocktails:

Shake the vodka, orange liqueur, blackberry purée, lime juice and simple syrup with ice cubes.

Strain into martini glasses. Garnish with an orange slice and serve immediately.